General information
| Catalog no.: | 00860721 |
| Credit points: | 3 |
| Prerequisite: | 00840738—Control Theory |
| Grading policy: | lecture-time quizzes—20% (magen, average of 5 best out of 6), provided the final exam is passed homework—40% (tokef, average of 3 best out of 4) final exam—40% (or 60%, if its grade is lower than 55) |
| Passing policy: | Minimum passing grade is 55; only those who submitted all homework solutions are eligible to take the final exam |
Lecturer
Leonid Mirkin, 653 Lady Davis Bld., phone: 3149, email:Classes
Wednesday, 17:30-20:20, room 283, Lady Davis Bld.Final exams
| Moed | Date | Time | Location |
|---|---|---|---|
| א׳ | Aug 4 | 9:00 | Lady Davis 658 |
| ב׳ | Sep 8 | 9:00 | Lady Davis 283 |
Syllabus
- linear algebra: sign definite matrices, block matrices, Schur complement, matrix equations (Sylvester, Lyapunov, Riccati)
- state-space realizations: canonical realizations, poles and zeros via realizations, connecting systems in state space
- structural properties of realizations (controllability, observability, minimality, etc)
- modal state feedback ideas: Ackermann's formula, quadratic Lyapunov functions and LMIs (linear matrix inequalities)
- optimization-based state feedback ideas: finite- and infinite-horizon LQR, properties of the optimal solution
- state observers: full- and reduced-order, optimal observers (deterministic Kalman filter)
- observer-based feedback, LQG, system design via LQG
- handling disturbances: disturbance observers, internal-model control, H-inf state feedback
- introduction to MPC (Model Predictive Control)
both continuous- and discrete-time results will be studied for most topics
Literature
- Åström K. J. and R. M. Murray. Feedback Systems: An Introduction for Scientists and Engineers, Princeton U Press, 2008
- Åström K. J. and B. Wittenmark. Computer-Controlled Systems: Theory and Design, Prentice Hall, 1997
- Kwakernaak H. and R. Sivan. Linear Optimal Control Systems, John Wiley & Sons, 1972
Lectures
- a crash review of DS and CT material (my perspective)
- linear algebra: more and less familiar results (also in beamer mode)
- state-space realizations, system interconnections (also in beamer mode)
- state feedback regulation via pole placement; controllability and stabilizability (also in beamer mode)
- state feedback regulation via LQR, algebraic Riccati equations (also in beamer mode)updated 31.5.2026
m-file for the classes 4 and 5 - LQR solution and its properties (also in beamer mode)
- state-feedback regulation via quadratic Lyapunov functions and LMIs; state observers (also in beamer mode)
- observability, minimality, state observers (full- and reduced-order); observer-based feedback (also in beamer mode)
- tracking; disturbances: exosystems, regulator equation, internal-model control (also in beamer mode)
- state observers under disturbances and noises, Kalman–Busy filter, LQG (also in beamer mode)
- H-inf state feedback, filtering, output feedback (also in beamer mode)
- discrete-time control and estimation in state space (also in beamer mode)
- discrete-time control and estimation in state space (contd) (also in beamer mode)
Homework assignments
- homework 1 (submission deadline: May 27, 13:00)
- homework 2 (submission deadline: Jun 23, 20:00)
- homework 3 (submission deadline: Jul 8, 13:00)
- homework 4 (submission deadline: Jul 24, 13:00)
Exams
- Examples of exam questions